Slow slip and tremor search at Kilauea Volcano, Hawaii

Authors


E. K. Montgomery-Brown, Department of Geoscience, University of Wisconsin–Madison, 1215 W. Dayton St., Madison, WI, 53706 USA. (emilymb1@gmail.com)

Abstract

[1] Kilauea Volcano, Hawaii, has hosted a long series of slow slip events observed since the installation of the continuous GPS network in 1996. Kilauea's slow slip events are inferred to occur on the decollement fault at 8 km depth beneath its south flank, with a location updip of the epicenters of large, regular earthquakes. Fault slip typically lasts about two days, and the events have magnitudes equivalent to Mw 5.3–6.0. While slow slip events in subduction zones are commonly accompanied by tectonic tremor (also called nonvolcanic tremor), no tremor has yet been reported in association with Kilauea's slow slip events. Instead, there are swarms of small triggered earthquakes, which is a characteristic only seen at select subduction zones (e.g., Boso and Hikurangi). A temporary array of seismometers was installed at Kilauea in 2007 in anticipation of a slow slip event. Here we use several established methods to perform a systematic search for tectonic tremor during geodetically defined slow slip events, as well as searching for tremor triggered by teleseismic surface waves. We do not detect tectonic tremor using any of these methods, although we are able to detect episodes of previously identified deep offshore volcanic tremor at 15–20 km depth and volcanic tremor from Kilauea. Although Kilauea's seismic network may not be adequate to observe tectonic tremor because Hawaii is seismically noisy and its crust is highly attenuating, it is also possible that the specific fault conditions on Kilauea's decollement are not conducive to such tremor generation.

1 Introduction

[2] In subduction zones worldwide, tectonic (or nonvolcanic) tremor commonly accompanies episodes of slow slip [Schwartz and Rokosky, 2007] (Figure 1). Tremor in general is recognized on seismograms as emergent, low amplitude, and long duration signals that are enhanced in frequencies between 1 and 10 Hz, while being deficient in higher frequencies common to small earthquakes. We would like to note that tremor observations are thought to originate from either fault slip or fluid migration. Here we refer to these two sources as tectonic tremor and volcanic tremor, respectively.

Figure 1.

Locations where tremor and slow slip events have been observed. Black arrows show locations where slow slip and tremor have been observed together, while red arrows show locations that host slow slip events, but lack tremor observations. Map is roughly based on the review map in Schwartz and Rokosky [2007] with additions from Brudzinski et al. [2010], Rubinstein et al. [2010], and Beroza and Ide [2011]. Slow slip at Parkfield is inferred from tremor activity [Smith and Gomberg, 2009]. San Juan Bautista has shallow slow slip but no tremor [Gomberg et al., 2009]. Long-term slow slip zones in SW Japan (Bungo and Tokai) have tremor detected at their downdip edges only [Hirose and Obara, 2005, 2006].

[3] Tectonic tremor was discovered by direct observation in the seismic waveforms [Obara, 2002], and also by association with geodetically observed slow slip events [Rogers and Dragert, 2003] (Figure 1). In other regions, tremor triggered by the passage of surface waves from large teleseismic earthquakes was the first indication of such behavior [Gomberg et al., 2008].

[4] Table 1 lists typical durations and slip magnitudes for worldwide slow slip events. Slow slip events in subduction zones in Cascadia and Shikoku, Japan occur at the transition between the locked zone and the stably sliding fault downdip. Rate-and-state friction laws have been used to model slow slip events (Kuroki et al. [2004], using methods from Tse and Rice [1986]). Varying the velocity cutoff and changing the frictional characteristics from velocity weakening to velocity strengthening can produce short-term slow slip events [Kato, 2003; Shibazaki and Iio, 2003; Shibazaki and Shimamoto, 2007], but Liu and Rice [2007] showed that events can also arise spontaneously near the base of the seismogenic zone. Liu and Rice [2007] and Rubin [2008] explored frictional conditions further and concluded that low effective stresses and a large slip-weakening distances are favorable for slow slip generation.

Table 1. Slow Slip Estimates and Duration Data. Average Velocities Computed From Slip and Duration
LocationSlip (cm)Duration (days)Velocity (m/s)Tremor
  1. aMontgomery-Brown et al. [2009].

  2. bSchwartz and Rokosky [2007].

  3. cKim et al. [2011].

  4. dPayero et al. [2008].

Kilauea, Hawaii, USAa151.5–2.210− 6N
Bungo (short), Japanb2–44–1010− 7Y
Guererro, Mexicob3020010− 7Yd
Gisbourne, New Zealandb,c181010− 7Y
Alaska, USAb12–16100010− 7Y
Tokai, Japanb0.08–1.83–510− 8Y
Cascadiab2–86–1510− 8Y
Bungo (long), Japanb5–2090–30010− 8Y
Boso, Japanb5–2050–20010− 8N
Costa Ricab1.53010− 9Y

[5] Slow slip events may provide important information for forecasting future large earthquakes. For example, Vidale and Houston [2012] suggested that understanding slow slip events could help narrow the warning time window for a great earthquake, or that it is possible that slow slip events could be a manifestation of the stress accumulation process before a great earthquake. A supporting observation was made prior to the M9.0 Tohoku-Oki earthquake in Japan where Kato et al. [2012] reported that two slow slip transients, manifested as migrating swarms of small earthquakes, propagated toward the eventual hypocenter in the days leading up to the earthquake. In addition to slow slip events, Kilauea's decollement hosts large earthquakes (e.g., the 1975 Mw 7.7 Kalapana earthquake [Nettles and Ekström, 2004]), therefore, improving forecasting capabilities would be helpful at Kilauea.

[6] While tectonic tremor and slow slip often occur together, their physical relationships to one another are still uncertain. Ito et al. [2007] suggested that tectonic tremor is the superposition of seismic radiation from rupturing small asperities within the slowly slipping zone, with a yield stress that is reduced by high pore fluid pressures. In Cascadia, Bartlow et al. [2011] showed that tremor locations coincide in space and time with the geodetically determined positions of high slip rate, supporting the hypothesis that local asperities on the fault are loaded directly by surrounding slow slip.

[7] Tremor accompanies slow slip events with varying slip magnitudes, durations, and rupture velocities (Table 1). Although tremor was difficult to find in New Zealand, recent studies have documented tremor accompanying some of New Zealand's slow slip events [ Kim et al., 2011] and the occurrence of teleseismically triggered tremor [Fry et al., 2011]. Some episodes of afterslip have also been analyzed for tremor (e.g., Denali Fault in Alaska and northeast Japan) without any detection [Rubinstein et al., 2010; Gomberg et al., 2012]. Locations also exist where both slow slip events and tremor occur, but offset from each other (e.g., Mexico and Nankai [Kostoglodov et al., 2010; Hirose et al., 2010]).

[8] Tectonic tremor is proposed to be generated by shear slip on the plate interface [Ide et al., 2007]. Tectonic tremor events are suggested to lack high frequencies as a result of slow rupture and slip velocities, perhaps due to low shear stresses caused by high fluid pressures [Shelly et al., 2007] or high attenuation surrounding slow slip regions. Shelly et al. [2007] showed that nearly 80% of tectonic tremor waveforms could be template-matched by waveforms from known low frequency earthquakes (LFE). Meanwhile, Ide et al. [2007] showed that a stacked focal mechanism was consistent with plate interface slip. Brown et al. [2009] found that tremor locations in multiple subduction zones localized onto the plate interface. Additionally, the observed triggering from teleseismic surface waves supports the hypothesis that tremor results from shear slip on plate boundary faults [Hill, 2010].

[9] To understand the relationship between slow slip and tremor, it is not only important to study locations where they occur together, but also to identify regions where slow slip or tectonic tremor occur in isolation. Along with locations where tremor and slow slip have been observed together, Figure 1 shows locations where slow slip has been observed without tremor (excluding afterslip). There are relatively few cases where tremor has not been observed at the locations of slow slip events. The Boso Peninsula in Japan is likely one of the best monitored regions where tremor has not been observed [Ozawa et al., 2003] (Figure 1). Tremor also has not been observed during slow earthquakes in Sanriku-Oki [Kawasaki et al., 2001]. After their discovery of tremor in New Zealand, Kim et al. [2011] suggested that tremor should always accompany slow slip, and that a failure to observe it results from highly attenuating material (e.g., Bungo Channel). While tectonic tremor is common at other locations on the San Andreas, shallow slow slip near San Juan Bautista has not been associated with tremor [Gomberg et al., 2009]. Kilauea has a long sequence of 10 slow slip events from 1998 to 2010 during which preliminary visual inspection revealed no tremor [Montgomery-Brown et al., 2009].

[10] At some locations where tremor and slow slip are not observed together, slow slip events are accompanied by swarms of small triggered earthquakes (e.g., Kilauea and Boso). Swarms of small earthquakes were observed during slow slip events off the Boso peninsula where tremor has not been observed [Ozawa et al., 2003, 2007]. The triggered swarms at Kilauea are discussed in more detail below. At both Kilauea and Boso, the cumulative moment of each seismic swarm is much smaller than the geodetically determined moment of the slow slip events.

2 Kilauea

[11] Kilauea is a shield volcano whose major volcanic and tectonic features include a summit caldera, rift zones in the east and southwest, and east-west trending cliffs marking the head scarps of the large-offset Hilina normal fault system (Figure 2). Earthquakes beneath Kilauea's south flank cluster on a planar structure at about 8 km deep [Got and Okubo, 2003; Syracuse et al., 2010]. Steady state motion of the south flank [e.g., Owen et al., 2000] is likely accommodated by slip along a nearly horizontal fault at a depth similar to the earthquakes. A planar structure at the same depth was imaged by a shipboard seismic reflection survey spanning several tens of kilometers offshore; the reflections also illuminated what appears to be the toe of a landslide at its southern extent [Morgan et al., 2000]. This structure is interpreted as a decollement fault marking the interface between sea floor sediments and the overlying volcanic pile [e.g., Hill, 1969; Nakamura, 1980; Got and Okubo, 2003; Morgan and McGovern, 2003]. It is believed that this detachment is the fault that ruptured during Kilauea's two historic tsunami-genic M > 7 earthquakes in 1868 and 1975 [Ando, 1979; Furumoto and Kovach, 1979; Lipman et al., 1985], although it has been suggested that the 1868 event rupture must have extended beneath Mauna Loa as well [Wyss, 1988].

Figure 2.

Reference map showing major structural features of Kilauea volcano and the locations of seismometers. The USGS HVO seismic network is shown by the green triangles, whereas the 2007 temporary installation is shown in blue. The geometry of the small aperture array (blue star) is shown in the inset. The extent of slow slip for the 2010 event is indicated by the gradational blue as determined by a geodetic inversion presented in the text and is the same as Figure 4. The second inset gives a schematic cross-section of Kilauea describing terminology used in this paper. The star shows the nucleation locations of large earthquakes on Kilauea approximated from Harvey and Wyss [1986] and Bryan [1992].

2.1 Kilauea's Slow Slip Events

[12] Slow slip events were first discovered on Kilauea's south flank in the continuous GPS time series as accelerated southward displacements of up to 1.5 cm [Cervelli et al., 2002]. Subsequently, 10 slow slip events were identified in the period from 1998 to 2010 [Brooks et al., 2006; Montgomery-Brown et al., 2009; Poland et al., 2010]. Inversions of geodetic data indicate that the slow slip events likely occur as seaward slip on a nearly horizontal decollement fault at about 8 km depth [Montgomery-Brown et al., 2009] (Figure 2), interpreted as the contact between the base of the volcanic pile and the underlying Cretaceous seafloor sediments [Eaton, 1962]. Slip events produce up to 20 cm of seaward slip along this decollement, and seismic moments inferred geodetically are equivalent to regular Mw 5.3 to 6.0 earthquakes (Table 2).

Table 2. Slow Slip Events at Kilauea Between 1997 and 2011
YearMonthDayMagnitudeReferences
  1. 1. Segall et al. [2006]; 2. Brooks et al. [2006]; 3. Cervelli et al. [2002]; 4. Montgomery-Brown et al., [2009]; 5. Montgomery-Brown et al. [2010]; and 6. Poland et al. [2010].

199802205.32,4
199809195.71,2,4
199911215.52,4
200005295.34
200011095.81,2,3,4
200212175.62,4
200307035.41,2,4
200501266.01,2,4
200706185.74,5
201002015.96

[13] Slow slip events in many subduction zones are observed downdip of the locked region where great earthquakes nucleate. In contrast, at Kilauea slow slip events occur updip of the nucleation zone of large earthquakes (Figure 2) [Harvey and Wyss, 1986; Bryan, 1992]. This constitutes a special case where updip slow slip events can be well monitored by land-based geodetic and seismic networks.

[14] Kilauea's slow slip events have thus far been correlated with swarms of small earthquakes that begin about a day after the start of slow slip [Segall et al., 2006; Wolfe et al., 2007] and that relocate to a thin zone presumably defining the decollement (6.5–8.5 km) [Syracuse et al., 2010]. The cumulative moment of the swarm seismicity only accounts for a very small fraction of the total geodetically constrained moment of the slow slip [Segall et al., 2006]. While triggered swarms accompany all slow slip events on Kilauea, such swarms are rare or absent elsewhere (e.g., Southwest Japan and Cascadia). Our present search for tectonic tremor takes advantage of the availability of continuous seismic data for two slow slip events on Kilauea: 17 June 2007 and 2 February 2010, both of which were typically-sized slow slip events for Kilauea.

3 2007 Slow Slip Event Summary

[15] The 17 June 2007 slow slip event was anticipated based on the recurrence pattern of prior events, and a temporary network of seismometers (Figure 2) and GPS instruments were deployed to record it. Thus both temporary seismometer data and data from the U.S. Geological Survey (USGS) Hawaiian Volcano Observatory (HVO) seismic network are available for tremor detection analyses. Although this event was delayed for several months after the anticipated date, it occurred concurrently with a large magmatic rift zone intrusion [Brooks et al., 2008]. Other than occurring at the same time as the intrusion, the event magnitude and spatial pattern were very similar to the 2010 event discussed below. This time period is seismically noisy with intrusion-related volcanic tremor and increased seismicity. See Montgomery-Brown et al. [2010, 2011] for more information on the June 2007 event and geodetic modeling details.

4 2010 Slow Slip Event

[16] The 2 February 2010 slow slip event was only recorded by the HVO seismic network with fewer instruments close to the source region than in 2007. HVO's GPS and tilt instruments also recorded the slip event. The 2010 slow slip event was accompanied by a swarm of ~25 triggered earthquakes (Figure 3a) similar to the swarms that accompanied the prior slow slip events at Kilauea. 2010 seismic noise levels were lower than during the rift zone intrusion in 2007, but close to Kilauea caldera, noise levels were affected by Halemaumau tremor, which has been present since late 2007.

Figure 3.

(a) Cumulative flank earthquake counts during the February 2010 slow slip event. (b) Daily GPS positions from coastal GPS site KAEP for the February 2010 slow slip event. Error bars are 2σ. (c) Fault slip (blue) from a uniform dislocation model estimated directly from GPS phase measurements (30 s samples). Red is a simple fit of a ramp function to the slip model to estimate start and end times of the event (vertical lines).

[17] Displacements observed by GPS instruments during the 2010 slip event were largest at the coast, and produced a maximum displacement of 1.6 cm southeastward at coastal GPS sites (e.g., KAEP in Figure 3b, and PGF4). Here we model the slip using the same methods as Montgomery-Brown et al. [2009] for a static, distributed slip model, and a kinematic time-dependent model with uniform slip.

[18] The distributed slip fault is modeled as a planar dislocation [Okada, 1985] that is subdivided into 2 km square subfaults (Figure 4). While the model is kinematic, it does include the effects of layered elastic structure (assuming a Poisson's ratio of 0.25) and topography. The model is smoothed with a Laplacian operator with a weight chosen by the L-curve criterion [Hansen, 1992]. The resulting maximum slip in the distributed model is 10 cm of seaward slip occurring about 5 km offshore (Figure 4).

Figure 4.

Distributed slip model of the 2010 slow slip event from GPS data. Black vectors are observed displacements, and red vectors show displacements predicted by the model. Error ellipses show the 2σ observational errors (about 1–2 mm in the horizontal directions). The intensity of the blue color indicates the amount of seaward fault slip (maximum 10 cm).

[19] The kinematic time-dependent model uses a single planar dislocation. We estimate the amount of slip in each 30 s epoch using a Kalman filter method developed by Cervelli et al. [2002]. Although significant improvements have been made in the last few years for processing subdaily (30 s sampling rate in this case) GPS positions on volcanoes [e.g., Larson et al., 2010], displacements during Kilauea's slow slip events are still smaller than typical noise levels in subdaily solutions on Kilauea. Instead of computing individual GPS positions, x, Cervelli et al. [2002] replaced the change in position, δx(t), with δx(t) = Gs(t) in the GPS observation equation, where s(t) is the fault slip and G is a matrix of elastic Green's functions relating modeled fault slip to surface displacement. The GPS carrier phase, Φ(t), and pseudorange, P(t), observables (notation from Hofmann-Wellenhof et al. [1990]) sampled every 30 s, are modeled as

display math(1)
display math(2)

where ro are the predicted double-differenced ranges from the stations to the satellites, the matrix, A, of partial derivatives relate the double-differenced ranges to corrections in the station coordinates, δx(t), which vary through time, z is the time-varying tropospheric zenith delay, mw is a tropospheric mapping function, and N are the sums of the integer phase ambiguities at the two GPS frequencies with wavelength λ. This method improves the signal-to-noise ratio of the slip signal by effectively replacing 3 × number of GPS stations with a single free parameter (fault slip).

[20] The resulting time-dependent slip model (30 s samples) is shown in Figure 3c. Based on a least squares fit of a ramp function to the subdaily slip model, the 2010 slow slip event began on day 31.6 of 2010, and lasted 3.2 days, which is longer than most previous slow slip events at Kilauea. As is typical at Kilauea, the triggered earthquakes began about a day after the slow slip started.

5 Seismic Data

[21] Here we analyze seismic waveform data during two slow slip events, 17 June 2007 and 2 February 2010. There were no complete continuous waveforms available for earlier slow slip events at Kilauea. Both events were recorded by the HVO seismic network (Figure 2). On Kilauea's south flank, the network consists primarily of single component short period instruments. In 2007, there was also a temporary network of broadband seismometers (Guralp CMG6TD and Guralp CMG40T, see Table 3) that were deployed with the intention of observing the anticipated slow slip event. All sites were sampled at 100 Hz. Our study represents the most systematic search to date for tectonic tremor at Kilauea.

Table 3. Station Locations and Sensor Types From the 2007 Temporary Deployment of Broadband Instruments
StationLatitudeLongitudeSensor
SEQA119.3218–155.2363CMG6TD
SEQA219.3233–155.2355CMG6TD
SEQA319.3218–155.2345CMG6TD
SEQA419.3228–155.2362CMG6TD
SEQA519.3226–155.2347CMG6TD
SEQA619.3213–155.2354CMG6TD
SEQA719.3223–155.2414CMG40T
SEQA819.3267–155.2206CMG40T
SEQ0119.2750–155.1549CMG40T
SEQ0219.3039–155.1556CMG40T
SEQ0319.3149–155.1284CMG40T
SEQ0419.3405–155.1609CMG40T
SEQ0519.2653–155.2089CMG40T
SEQ0619.2817–155.1929CMG40T
SEQ0719.3228–155.1941CMG40T
SEQ0819.2915–155.2231CMG40T
SEQ0919.3134–155.2227CMG40T
SEQ1019.3196–155.2558CMG40T
SEQ1119.2835–155.2443CMG40T
SEQ1219.2779–155.2824CMG40T

6 Methods and Results

[22] Tectonic tremor has been discovered and analyzed in locations worldwide using a variety of methods including:

  1. Waveform envelope cross-correlations where envelopes of the tremor waveforms are cross-correlated to determine arrival times [Obara, 2002; Wech and Creager, 2008],
  2. Template matching where LFEs are matched through the entire set of waveforms [Shelly et al., 2007],
  3. Autocorrelation where entire waveforms are autocorrelated to detect extended time periods of repeating seismic signals [Brown et al., 2008], and
  4. Beamforming where a tight cluster of seismometers is used to back project the direction from which seismic energy is coming [Ghosh et al., 2009a].

[23] We apply the above common methods to search for tremor during Kilauea's slow slip events, as well as moving window cross-correlation [Buurman and West, 2010]. We also include a search for tremor triggered by the surface waves from large, teleseismic earthquakes. Waveform data are analyzed from both the HVO seismic network and from the 2007 temporary network. The vertical and horizontal components are analyzed separately because many of the HVO stations only have a single, vertical component.

7 Envelope Method

[24] Tremor appears as an emergent signal in bandpassed seismic envelopes with elevated amplitudes lasting longer than typical earthquake coda. Waveform envelopes analyzed here are produced by adapting the method of Wech and Creager [2008] in which the signal is bandpassed between 2–8 Hz. Then we take the absolute value of the Hilbert transform, and finally low pass filter the envelope to 0.1 Hz. A threshold defining the level of background noise is computed from the mean value plus two times the standard deviation of a two hour quiet period before the slow slip event starts (as determined by geodetic inversions). Any waveforms exceeding this threshold for longer than two minutes are further analyzed.

[25] Using the envelope method, we discovered several similar, extended duration episodes of elevated envelope amplitudes in the continuous broadband 2007 data and the 2010 short period data. One example from 2007 is shown in Figure 5. These bursts typically last 10–30 min. They are frequently emergent, but can occasionally begin with an impulsive event. Only one example was recorded in 2007, but in 2010 there were several bursts before, during, and after the slow slip event with no discernible changes. Initial locations of these tremor bursts with a one-dimensional velocity model are several kilometers offshore and to the south of Kilauea caldera (example from 2010 tremor burst in Figure 6). Their depths range between 7.4–35 km, which is significantly deeper than the slow slip events. Aki and Koyanagi [1981] reported deep volcanic tremor in this area before, with similar durations, amplitudes, and locations. They interpreted these events as magma transport through the deep lithospheric plumbing system. Dzurisin et al. [1984] noted the correlation between these tremors and the shallow magma supply rate at Kilauea, further supporting their volcanic origin. Tectonic tremor was, however, unknown at the time of their publication.

Figure 5.

Seismograms (blue) with 2–8 Hz envelopes (red) and one spectrogram from a deep offshore tremor burst during the June 2007 intrusion and slow slip event.

Figure 6.

Locations of deep offshore tremor from Aki and Koyanagi [1981] (blue stars) along with locations derived from this study using the envelope method (large red dots) and moving window cross-correlation method (small red dots). Locations from the envelope method are at the times of the five largest amplitude envelopes in the 30 min burst. Locations from the moving window cross-correlations are from each 10 s window. The histogram below shows the range of depths determined from the moving window cross-correlation method with the red vertical bars indicating the 95% bounds.

[26] We note that while south flank earthquakes at Kilauea are typical volcano-tectonic earthquakes that are enhanced in high frequencies, relative to rift zone earthquakes, small flank earthquakes can appear to be depleted in high frequencies, when in fact they are simply very small and dominated by the background noise spectra. We tested the frequency content of the earthquakes in the HVO catalog for one day in 2007 by computing the power spectra and comparing the energy in two bands: 1–5 and 8–12 Hz. While the overall pattern shows that flank earthquakes are enhanced in high frequencies relative to rift zone earthquakes, individual small earthquakes are easily misclassified and might be mistaken for tectonic tremor by an automated system. A similar analysis in 2010 shows a much clearer differentiation between the rift zone and flank earthquakes because there was significantly less volcanic tremor activity.

[27] We suggest that extra care be taken when employing envelope methods to compare the power in various frequency bands in areas where there is high attenuation or where the spectrum of the background noise is similar to tremor spectra (i.e., volcanic environments), and the area has frequent small earthquakes.

8 Beamforming Method

[28] The beamforming approach [Ghosh et al., 2009a] takes advantage of a tightly clustered array of six stations (Figure 2) that were part of the 2007 temporary deployment. The method searches over a range of small delay times in the north and east directions to maximize the sum of the waveforms across the array. When the waveforms are from a coherent source, the beam is focused and points toward the source of the seismic energy. This type of analysis is usually performed on narrow bandwidth waveforms, and in our case the waveforms are band pass filtered between 2–6 Hz.

[29] We tested the capabilities of the beamforming approach using the 2007 seismic array and S waves from example earthquakes. We included data from only the six stations within the small aperture array, and analyzed waveforms between the first S arrival and the following 5–10 s. We tested earthquakes from the summit area, east rift zone, and the south flank. We found that the test beams consistently pointed to within 15° of the earthquake location (Figure 7), which is sufficient to separate rift zone seismic energy coming from north of the array from potential flank seismic energy coming from south of the array. The beams decorrelated, however, if stations outside of the small aperture array (>500 m away, such as SEQA7 and SEQA8, Figure 2) were included. During bursts of volcanic tremor from the 17 June 2007 intrusion, the beam remained steadily pointing northward for extended periods of time, and coherency improved as a result of temporal averaging. The important conclusion from these tests is that we can distinguish whether the energy in the tremor bandwidth is coming from the summit, the rift zone, or the flank.

Figure 7.

Three example beams computed from the first S arrival and the following 5–10 s of waveform from known small earthquakes as a test of the beamforming method using the six station small aperture array (SEQA1-A6).

[30] We computed beams every 10 s for 6 h of seismogram data (starting 10 January 2010, 12:00:00), and then plotted the directions of the beams in the top 5% of amplitudes (the most focused beams). A large fraction of the beams point toward two known sources of seismic energy, the summit area and the east rift zone, but a remaining fraction of the beams point southwestward, suggesting that significant energy in the 2–6 Hz bandwidth is coming from an area to the southwest of the array.

[31] When using this method in Cascadia, Ghosh et al. [2009a] projected the beam onto the subduction interface to determine a location. Here for the 2007 tremor burst (Figure 5), we can compare the location of the beam projected onto the decollement with the locations determined from the envelope method and one from a standard location using picks from the impulsive first arrival. The time-averaged beam spanning the tremor episode produces an optimal slowness of 0.7 s/km coming from the southwest of the array. Assuming a uniform S-velocity of 3.3 km/s [Hansen et al., 2004], this optimal slowness corresponds to an incidence angle of 25°. Projecting this ray onto the decollement results in an epicenter about 4 km to the southwest of the array in an area where none of the other methods produce an epicenter. Instead, if we project the ray down to 20 km, consistent with the depths determined from the other location methods, then the epicenters overlay. Thus, we believe that the beams from the southwest of the array are from the deep tremor discussed above [Aki and Koyanagi, 1981].

9 Template Matching

[32] For this method, seismic signals from a known event are passed through the entire continuous waveform. Correlation values are computed and then summed over the entire observation network. Shelly et al. [2007] used catalog LFE locations from Japan as templates. Kilauea does not yet have any identified LFEs on the decollement fault.

[33] We attempted to find LFEs by analyzing the power spectra of flank earthquakes and other bursts of seismic energy. In 2007, nearly all detected flank earthquakes had typical volcano-tectonic frequency contents (enhanced in high frequencies), or were too small to separate from typical noise spectra. The average background noise is significantly enhanced in low frequencies associated with heightened magmatic activity. In 2010, there is a much clearer separation in the typical frequency contents of rift zone and flank earthquakes. Nonetheless, the flank earthquakes all have very similar spectra and none of them display the characteristic lower frequencies expected from tectonic tremor.

[34] We implemented this method in a test mode using regular volcano-tectonic flank earthquakes bandpass filtered from 2–8 Hz. Several templates have significant matches within the continuous waveforms, but they are mostly isolated events, and not over extended time periods. The isolated events are not surprising, since we are likely detecting additional small, noncatalog earthquakes. It is possible that developing methods utilizing the cepstrum [e.g., Brown and Beroza, 2011] may be able to detect LFEs on Kilauea in the future, which would make template matching more useful for detecting tectonic tremor at Kilauea.

10 Autocorrelation

[35] Autocorrelating an entire waveform can highlight times when similar signals repeat. Because tectonic tremor is composed of many repeating LFEs, autocorrelation can be used to detect repeating LFEs even when LFEs have not been previously detected [Brown et al., 2008]. The autocorrelation method is applied by autocorrelating 10 s windows of seismogram and then shifting the window ahead by 2 s. A long window is used because we do not know the origin time or move out of any potential LFEs. The autocorrelation values are summed across the network, and larger values indicate windows that have similar waveforms at all stations in the network and may contain candidate events.

[36] Once windows containing candidate events are detected, waveform cross-correlation is applied to all pairs of candidate waveforms at each station at the precision of the seismic sampling rate (0.01 s) to detect near repeats. The cross-correlation values are then summed across the network again.

[37] Autocorrelation of one day of data from the temporary broadband stations during the 2007 intrusion and slow slip event finds 863 correlated windows. Figure 8 shows an example of 590 well correlated waveforms detected by autocorrelation of 24 h of data on 18 June 2007 as they were observed at SEQ01. Many of the correlated windows occur during the same long burst of known deep tremor as seen in Figure 5. None of the other correlated windows extend for a long duration (roughly defined as greater than 1 min) that would suggest tremor.

Figure 8.

Example autocorrelation matches that were detected by autocorrelating 24 h of data on 18 June 2007. The 590 very well correlated waveforms are defined by having cross-correlation coefficients of greater than 15 (summed over the whole network of 14 three-component stations). The normalized velocity traces are overlayed in the top plot (gray) with the black line showing a stack. The same traces are shown below in shaded colors.

11 Moving Window Cross-Correlation

[38] To obtain regularly spaced delay times for well correlated windows (see Figure 9 for an example from the small aperture array SEQA1-SEQA8 in 2007), we applied a moving window cross-correlation method with the GISMO toolbox for MATLAB [Buurman and West, 2010], which is built on the Waveform Suite [Reyes and West, 2011]. We correlated waveforms relative to a master trace (SEQA1) in 10 s windows with 50% overlap and recorded the correlation value and lag time in each window. Poor correlations at SEQA7 and SEQA8 explain why the beams decorrelate when including these stations using the beamforming method.

Figure 9.

Moving window cross-correlation and lag times for a tremor burst during the 2007 temporary deployment. (top) Cross-correlation coefficients relative to SEQA1 where warm colors indicate that the signal is similar at all stations, while cooler colors indicate a lower correlation. (bottom) Corresponding lag times where yellows are near zero lag, red is advanced and blue is delayed relative to SEQA1. Color saturation corresponds to the above cross-correlation coefficients, where no lag times are displayed for poorly correlated signals.

[39] For a very similar tremor burst during the 2010 slow slip event for which we correlated waveforms from the HVO seismic network, we then converted the lag times into absolute arrivals, and inverted for preliminary locations. The moving window method provides a large number of measurements allowing us to visualize the scatter in the locations and depths (Figure 6). Preliminary locations for these bursts fall in the same location and depth ranges as obtained using the envelope method, and in the same area as the locations of the previously discovered deep tremor [Aki and Koyanagi, 1981] (Figure 6).

12 Summary

[40] Each of the methods detected some form of volcanic tremor at Kilauea, but not tectonic tremor on the decollement fault. Although the density of events detected by each individual method is dependent on the window and filtering parameters and cutoff thresholds chosen, the patterns detected by all of the methods are consistent (Figure 10). Preliminary locations of a prominent burst of tremor during the 2007 slow slip event suggest a previously identified deep offshore volcanic tremor source. During the rest of the 2007 slow slip event, the majority of the tremor emanated from either the summit or the rift zones. During the 2010 slow slip event, the deep offshore volcanic tremor source was also active, but no tremor was detected on the flank.

Figure 10.

Example 2 h waveform and envelope, which includes the deep volcanic tremor burst (Figure 5) at 4000–5000 s, with detections from autocorrelation, waveform envelope cross-correlation and beamforming.

13 Triggered Tremor

[41] Tremor triggered by the passage of large, teleseismic surface waves is also commonly observed in areas where background tectonic tremor is observed [Gomberg et al., 2008; Fry et al., 2011; Chao et al., 2012], and has even been discovered outside the spatial extent where slow slip has been detected geodetically [Gomberg et al., 2008]. Characteristic observations of teleseismically triggered tremor include pulsing bursts of increased tectonic tremor amplitudes often appearing in sync with peak surface wave amplitudes and large S-wave amplitudes [Hill, 2010].

[42] On Kilauea, there have been many opportunities (earthquakes with Mw > 7.5 and varying azimuths, Figure 11 inset) to observe potential triggered tremor in the data from the HVO seismic network. We also examined three events that were recorded by the 2007 broadband deployment. However, none of the studied events are associated with significant tremor-like seismic signals concurrent with the passage of the teleseismic surface waves, as has been observed in cases of teleseismically triggered tremor. In general, the amplitudes of waveforms high-pass-filtered above 2 Hz increase during the teleseism (Figure 11), but without the regular pulsing observed during triggered tremor episodes elsewhere. While most of the analyzed data was from single vertical component stations, raising the possibility of not detecting horizontally polarized triggered tremor, all three components were analyzed when available. For example, the Solomon Islands earthquake discussed below was recorded on the 2007 temporary array. Additionally, the theoretical surface wave amplitudes on Kilauea are comparable to other studies of triggered tremor [e.g., Gomberg et al., 2008; Ghosh et al., 2009a; Fry et al., 2011].

Figure 11.

Example of a teleseism from the Solomon Islands Mw 8.1 (1 April 2007). Raw, band-passed (2–15 Hz) and high-passed (>1 Hz) waveforms from SEQA8 (top), and the spectrogram of the high-passed waveforms (bottom). Vertical lines indicate predicted arrivals of different phases from the NEIC based on the IASP91 Earth model [Kennett and Engdahl, 1991]. Inset: Radial coverage of teleseisms analyzed for triggered tremor. Angle shows the station to source azimuth while the radius is the log of the theoretical 1 s period body wave (open circle) and 20 s period surface wave (asterisk, when available). Events include: (a) Solomon Islands (Mw 8.1, 1 April 2007), (b) Vanuatu (Mw 7.2, 1 August 2007), (c) Java, Indonesia (Mw 7.5, 8 August 2007), (d) Ica, Peru (Mw 8.0, 15 August 2007), (e) Santa Cruz Islands (Mw 7.2, 2 September 2007), (f) Southern Sumatra (Mw 8.5, 12 September 2007), (i) Mariana Islands (Mw 7.5, 28 September 2007), (j) Auckland Islands (Mw 7.4, 30 September 2007), (k) Northern Mariana Islands (Mw 7.2, 31 October 2007), (l) Northern Chile (Mw 7.7, 14 November 2007), (m) Martinique (Mw 7.4, 29 November 2007), (n) Kermadec-Tonga (Mw 7.8, 9 December 2007), (o) Andreanof (Mw 7.2, 19 December 2007), (p) Simeulue (Mw 7.4, 20 February 2008), (q) Padang, Sumatra (Mw 7.2, 25 February 2008), (r) Xinjiang-Xizang (Mw 7.2, 20 March 2008), (s) Loyalty Islands (Mw 7.3, 9 April 2008), (t) Macquarie Island (Mw 7.1, 12 April 2008), (u) Eastern Sichuan (Mw 7.9, 12 May 2008).

[43] In the example waveform from the Solomon Islands earthquake (Figure 11), there are increased amplitudes at high frequencies that begin with the arrival of the P wave, but no anomalous signals during the surface wave arrivals. Ghosh et al. [2009b] showed triggering at Parkfield with stacked spectrograms during the arrival of the PKP, PP, SKP, and SKS groups after Sumatra, but those triggered tremor signals were followed by even larger amplitude tremor during the surface waves. At Kilauea, the high-passed waveforms do not show elevated amplitudes during the passing surface waves (Figure 11).

14 Discussion and Conclusions

[44] Hypotheses on the origins of slow slip and tectonic tremor are summarized in detail by Beroza and Ide [2011]. Here we do not attempt a complete review, but simply present a few hypotheses that may directly relate to the environment at Kilauea. Two options may explain why we have not observed tectonic tremor associated with Kilauea's slow slip events: (1) tremor is generated, but it is below the detection threshold or, (2) Kilauea's slow slip events do not generate tectonic tremor, although they trigger small earthquake swarms.

[45] If we lack the capability to observe tremor on Kilauea, there are several explanations including high background noise levels and high seismic attenuation in the highly fractured basalts, which may contribute to a poor observational environment for tectonic tremor detection. Perhaps the temporary deployment in 2007 was not dense enough to boost the SNR of the potential tremor. In anticipation of another slow slip event in 2012, we deployed a second small aperture array of sixteen sites which will be the subject of future work.

[46] Kilauea is on an ocean island and thus is a very noisy seismic environment. All of the stations used to observe potential tremor are relatively close to the coast. While most subduction zone tremor observations do not report amplitudes, Shelly et al. [2007] show tremor and LFE spectra compared with noise spectra in Japan. Below 1 Hz, the background noise amplitudes are about the same order of magnitude as both the LFE and tremor amplitudes (∼ 10− 6 m s− 1 Hz− 1). Above 1 Hz, the noise amplitude drops off quickly to ∼10− 7 m s− 1 Hz− 1, while LFE and tremor amplitudes remain higher. Similar spectra from New Zealand by Kim et al. [2011] (in dB) and for Cascadia by Kao et al. [2005] (normalized amplitudes), show less than an order of magnitude difference between tremor and noise signals between 2 and 6 Hz. At Kilauea on the temporary network in 2007, we estimate noise levels of ∼ 10− 6 m s− 1 at 2 Hz, but noise levels drop to inline image m s− 1 at frequencies > 5 Hz on many stations.

[47] Explanations for why Kilauea and New Zealand (prior to recent results discussed below) lacked tectonic tremor included speculations about the pressure being lower due to shallow depths and temperature conditions being cooler than the subduction zones in Cascadia and southwest Japan. Triggered tectonic tremor has since been discovered in the Hikurangi, New Zealand [Fry et al., 2011] and accompanying a slow slip event in March 2010 [Kim et al., 2011].

[48] In light of the suggestion from Kim et al. [2011] that high attenuation can degrade tectonic tremor signals, we summarize the available ranges of Q for some example subduction zones to compare with Kilauea. Since tectonic tremor is comprised mostly of S-waves, Qs would be most relevant to compare. However, not all attenuation studies report Qs , so we report Qs when it is available, and substitute Qp otherwise.

[49] Attenuation tomography results show that Kilauea is highly attenuating (low Q values) with both Qp and Qs ranging from 50 to 250 [Hansen et al., 2004]. The Hikurangi subduction zone is also highly attenuating with Qp ranging from 50 to 400 in the overriding plate, and 600 to 1500 in the subducting slab [Eberhart-Phillips et al., 2008]. The Boso Peninsula, which lacks tremor, is also highly attenuating with Qs of 100 at 0.8 Hz in a frequency-dependent attenuation model [Kinoshita, 1994]. In the Bungo Channel, where tremor is prevalent [Hirose and Obara, 2005], Salah and Zhao [2003] find Qp values of 400 to 1500. Although high attenuation may contribute to the difficulty in observing tectonic tremor at Kilauea, it is not likely the only factor obscuring the observation because we observed the difference in frequency content between rift zone and flank earthquakes when we implemented the envelope method.

[50] We believe it is possible that Kilauea's absence of tremor could result from specific conditions on the decollement fault. We reiterate here that slow slip occurs in the shallow updip region of the fault, whereas in subduction zones it is observed downdip of the locked zone. Possible factors limiting the generation of tremor at Kilauea might include slip velocity, pressure and temperature conditions, availability of fluids to reduce friction on the decollement, or a lack of asperities. All of these factors can contribute to the frictional state of the fault and whether there are transitions from velocity weakening to velocity strengthening that may generate slow slip events.

[51] At 10–15 cm Kilauea's slow slip events have larger total fault slip than in Cascadia (2–5 cm [Schmidt and Gao, 2010]), Tokai (3 cm [Hirose and Obara, 2006]), or Hikurangi (1.5–15 cm [Wallace and Beavan, 2006]). Slip velocities of Kilauea's slow slip events (10–6 m/s) are faster than those in subduction zones (Table 1). It is possible that rupture velocities coinciding with these slip rates are too fast to generate tremor at Kilauea. Slip velocities in Boso (10− 8 m/s), where tremor is also not observed, are slower than in Cascadia and other locations in Japan. Slip events in Costa Rica are even slower (10− 9 m/s), however, tremor in Costa Rica occurs not only during slip events, but also is nearly continuously present between geodetically observable slip events [Walter et al., 2011]. These contradictory examples suggest that while slip velocities may contribute to the occurrence of tremor, slip velocity is not the only controlling factor.

[52] In the Japan and Cascadia subduction zones, pressure and temperature paths [Peacock, 2009] are different from each other, but each pass through several phase changes that release water. At Kilauea, the slow slip events are much shallower (8 km, ~0.25 GPa), so pressures are much lower than in Japan (30–40 km, ~0.8–1.2 GPa) and Cascadia (30–40 km, ~0.8–1.2 GPa) [Peacock, 2009]. The slow slip events in New Zealand are the only other observed events that extend updip as shallow as ~10 km, and maybe shallower [McCaffrey et al., 2008]. Slow slip events in Boso are also relatively shallow, with slip extending updip to ~20 km [Sagiya, 2004].

[53] Slow slip events occur in Japan in the temperature range of 290–450°C [Spinelli and Wang, 2008; Peacock, 2009; Spinelli and Harris, 2011], while in Cascadia temperatures range from 410–550°C [Peacock, 2009; Cozzens and Spinelli, 2012]. Slow slip events exist at cooler temperatures in Costa Rica [Harris et al., 2010] and New Zealand's shallower slow slip events [Fagereng and Ellis, 2009]. Temperatures on Kilauea's decollement are relatively unknown and may be more complex than typical intraplate geotherms because of the active volcanic system.

[54] While initial hypotheses related tectonic tremor to fluid flow because of the similarity to volcanic tremor [Kao et al., 2005], more recent evidence indicates that tectonic tremor is composed of shear slip events [Ide et al., 2007; Brown et al., 2009; Hill, 2010]. However, pressurized pore fluids likely still play an important role in reducing the effective stress on the slipping fault plane [Shelly et al., 2006; Matsubara et al., 2009]. Water on Kilauea's decollement likely comes from compaction of the pelagic sediments under the weight of the volcanic pile. It is possible that there is too little or too much fluid on Kilauea's decollement to generate tremor.

[55] In subduction zones, overriding plate composition may also be important. Brudzinski and Allen [2007] noted that the segmentation of slow slip events in Cascadia was related to the composition of the overriding plate. For example, they suggest that slow slip events under the more mafic Siletzia terrane have longer recurrence intervals than the continental Klamath terrane because the Siletzia is denser and stronger [Brudzinski and Allen, 2007]. In Japan, Kato et al. [2010] noted that the Moho discontinuity divides the Tokai slow slip events and tremor into shallower and deeper sections with differing behaviors. It is possible that contact between the sediments and Kilauea's volcanic edifice may not host asperities with sufficient integrity to rupture and radiate seismic energy during slow slip events.

[56] In conclusion, although we detect plenty of volcanic tremors on Kilauea using common methods, tectonic tremor still has not been observed. Such lack of tremor might be related to specific physical and rheological conditions on the decollement, but waveform data from the 2007 and 2010 slow slip events do not eliminate the possibility that tremor occurs below the current detection threshold.

Acknowledgments

[57] Temporary seismic data were collected during 2007 with support from an NSF SGER grant, while data from the backbone monitoring network at the Hawaiian Volcano Observatory is supported by the USGS. We thank Lee Powell, Russell Sell, Chris Dietel, Jeremy Pesicek, Seung-Sep Kim and Michael Chandler for their help with the field deployment. This research was supported by a National Science Foundation (NSF) Post-doctoral Fellowship #EAR-0846959, and NSF grants #EAR-0910532, #EAR-0910469 and #EAR-0712864. We would also like to acknowledge discussions with P. Segall regarding installation of the array and possible tremor mechanisms at Kilauea, and assistance from J. Brown with the autocorrelation.

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